Direction indices

From Online Dictionary of Crystallography

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Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the '''direction indices'''.
Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the '''direction indices'''.
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In the three-dimensional space, the direction passing through the origin and the lattice nodes ''nu'',''nv'',''nw'', where ''n'' is an integer, has direction indices [''uvw'']. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-''u'', -''v'' and -''w''] identify the same direction as [''uvw''] simply observed from the opposite side.
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In the three-dimensional space, the direction passing through the origin and the lattice nodes ''nu'',''nv'',''nw'', where ''n'' is an integer, has direction indices [''uvw'']. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-''u'', -''v'', -''w''] identify the same direction as [''uvw''] simply observed from the opposite side.
When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.
When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.

Revision as of 10:16, 1 September 2017

Indices de direction (Fr); Indices de dirección (Sp); Indici di direzione (It); 方向指数 (Ja).


Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the direction indices.

In the three-dimensional space, the direction passing through the origin and the lattice nodes nu,nv,nw, where n is an integer, has direction indices [uvw]. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-u, -v, -w] identify the same direction as [uvw] simply observed from the opposite side.

When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.

See also